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Grid Free Lagrangian Blobs Vortex Method With Brinkman Layer Domain Embedding Approach for Heterogeneous Unsteady Thermo Fluid Dynamics Problems
Carmine Golia, Bernardo Buonomo, Antonio Viviani
Pages - 313 - 329     |    Revised - 05-08-2009     |    Published - 01-09-2009
Volume - 3   Issue - 3    |    Publication Date - June 2009  Table of Contents
Buoyant plume/Body interaction, Thermal/Vortex Blobs, Brinkman domain embedding
Modeling unsteady thermal–viscous flows inside/around complicated geometries containing multiphase sub-systems (fluid–porous–solid) and multi-physics phenomena (diffusion; forced/free/mixed convection; time variations of velocity, temperatures and heat fluxes sources; still and moving bodies) is an ambitious challenge in many applications of interest in science and engineering. Scope of this exploratory work is to investigate if the combination of a grid free Lagrangian Blob method with a Brinkman layer domain embedding approach can be useful for the preliminary analysis of heterogeneous unsteady thermal buoyant problems, where easiness, readiness, short computational times, good qualitative and sufficient quantitative accuracy are the most important aspects. In this work we couple a grid free unsteady Lagrangian Thermal-Vortex Blob method with a double penalization method that considers solid bodies contoured by a fictitious buffer thin boundary layer, described by a porous Brinkman model. The model problem in this study is the interaction of a thermal buoyant plume with a solid body, still or in motion. Both solid body and Brinkman boundary layer are described by volume penalization applied by an unsteady mask method. After a description of this novel approach, preliminary analyses for validations are presented for various thermal buoyant steady/unsteady problems relative to thermal and thermal-vortical patches, fixed, free and in presence of a still or moving body. Comments on pros, contras and further work, conclude the paper.
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1. Arquis,E. ,Caltagirone,J-P., Vincent,S : Sur le conditions hydrodynamique au voisinage d'une interface millieux fluid-millieux poreux: application à la convection naturelle, C.R. Acad. Sci. Paris, 1984, Series II, 299: 1-4
10. Schneider,K. : Numerical simulation of the transient flow behaviour in chemical reactors using penalization method, Computer and Fluids, 2005, 34: 1223-1238
11. Vasilyev,O.V , Kevlahan, N.K.R.,: Hybrid wavelet collocation-Brinkman penalization method for complex geometry flow, , International Journal for Numerical Methods in Fluids, 2002, 40 : 531-538
12. Kevlahan, N.K.R., Vasilyev,O.V., Goldstein, D., Jay, A.: A adaptive wavelet collocation method for fluid-structure interaction at high Reynolds number, SIAM J. Sci. Comp., 2005, 6, 34-??
13. Kevlahan, N.K.R., Ghidaglia JM. : Computation of turbulent flow past array of cylinders using spectral method with Brinkman penalization, Eur. J. Mech. B - Fluids, 2001, 20 :333-350
14. Bruneau,C.H. , Mortazavi I.: Control of Vortex Shedding Around a Pipe section Using a Porous Shealth, International Journal of Offshore and Polar Engineering, 2006, 16: 90-96
15. Chiavassa G. , Donat R. ,: Point Value Multiscale Algorithms for 2D Compressible Flow, Siam J. Sci. Comp. 2003, 23 : 3
16. Bruneau,C.H. , Mortazavi I.: Controle passif d'ecoulement autour d'obstacles par les milieux poreaux, Comptes rendus de l'academie de Sciences, 2001, 329 :517-521
17. Bruneau,C.H. , Mortazavi I.: Passive control of the flow around a square cylinder using porous media, Int. J. Numer. Methods Fluids, 2004, 46: 415-433
18. Carbou,G. , Fabrie P : Boundary Layer for a penalization method for viscous compressible flow, Adv. Differential Equations, 2003, 8 :1453
19. Carbou,G. : Penalization method for viscous incompressible flow around a porous thin layer, Nonlinear Anal. Appl., 2004, 5: 815-855.
2. Angot, Ph.: A Mathematical and numerical modelling for a fictious domain method with penalized immersed boundary conditions, HDR thesis, Universitè Mediterranée, Aix-Marseille,1998
20. Carbou,G. : Brinkman Model and Double Penalization Method for the Flow around a Porous Thin Layer, J.Math. Fluid. Mech., 2008, 10: 126-158
21. Cottet,G.H. and Koumoutsakos,P.D.: Vortex Methods: Theory and Practice, Cambridge University Press, 2000.
22. Golia,C., Buonomo,B., Manca,O., Viviani,A. A Vortex-Thermal Blobs Method For Unsteady Buoyancy Driven Flows. ASME-IMECE, Anaheim (CA), 2004.
23. Golia,C., and Buonomo,B. An Effective Blob Approach to Unsteady Thermal Buoyant Flow. CMEM, Malta, 2005.
24. Golia,C., and Buonomo,B. Numerical Simulation of Unsteady Natural Convection by Blobs Methods. 60th ATI Congress, Roma, 2005.
25. Golia,C. and Buonuomo,B. On the accuracy of integral representation of differential operators in meshless Lagrangian blob method. CMEM, Praga, 2007.
26. Chorin, A.J. Numerical Study of Slightly Viscous Flow. J. Fluid Mechanics 1973; 57 (4) : 785-796.
27. Chorin, A.J. Vortex sheet approximation. J. Comp. Phys. 1978; 27 : 428-442.
28. Rokhlin,V. Greengard, L. A fast algorithm for particle simulation. J. Comp. Phys. 1987; 73 : 325-348
29. Degond,P. and Mas-Gallic,S. The weighted Particle method for Convection-Diffusion Equations, part.1: the case of an isotropic viscosity. Math.s of Computation 1989; 53 (188) : 485-507
3. Angot, Ph., Bruneau C.H., Fabrie, P.: A penalization method to take into account obstacles in incompressible viscous flows, Numerische Mathematik, 1999, 81(4): 497-520
30. Eldredge,J.D., Leonard,A. and Colonius,T. A General Deterministic Treatment of Derivatives in Particle Methods. J. Comp. Phys. 2002; 180: 686-709
31. Meijering, E., Unser, M. A Note on Cubic Convolution Interpolation. IEEE Trans. Image Process. 2003; 12 (4): 477-479.
32. G.K. BatcheloR: “An Introduction to Fluid Dynamics”, Cambridge Univ. Press, pp. 534 (1967).
33. G. Riccardi, C, Golia: Integral Balance Laws for 2D buoyancy driven flows. VII SIMAI Congress, Venice, 2004.
4. Caltagirone,J-P., Vincent,S : Sur une methode de penalisation tensorielle pour la resolution des equations de Navier-Stokes, C.R. Acad. Sci. Paris, 2001, t.329, Series II b: 607-613
5. Khadra, K., Angot,Ph., Parneix, S., Caltagirone,J-P.: Fictitious domain approach for the numerical modeling of Navier-Stokes equations, International Journal for Numerical Methods in Fluids, 2000, 34: 651-684
6. Schneider,K. ,Farge, M. : Coherent Vortex Simulation (CVS) of a 2D bluff body flow using an adaptive wavelet method with penalisation, Advances in Turbulence, 2002, 9: 471-474
9. Schneider,K. ,Farge, M. : Numerical simulation of transient flow behaviour in tube bundles using volume penalisation method, J.Fluids and Structures, 2005, 20 (4): 555-566
Schneider,K. ,Farge, M. : Adaptive Wavelet Simulation of a flow around an impulsively started cylinder using Penalization; Applied and Computational Harmonic Analysis, 2002, 12: 374-380
Schneider,K. ,Farge, M. : Numerical simulation of dipole-wall interaction using an adaptive wavelet discretizatuion with volume penalisation, ENUMATH, 2005, eds.Bermudiz et alia, Springer, 822-830
Professor Carmine Golia
- Italy
Dr. Bernardo Buonomo
- Italy
Professor Antonio Viviani
- Italy

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